Vibrational States of the Hydrogen Molecular Ion

The eigenvalues and eigenfunctions of the vibrational states belonging to the ground electronic state of the hydrogen molecular ion have been calculated. The calculations have been done for the $J=0, 2, 4, \mathrm{and} 7$ rotational states. Included is a discussion of the dependence of the eigenvalues as a function of the lowest-order dynamic corrections to the internuclear potential. Also, a calculation has been done to determine the number of bound states of the ${\mathrm{D}}_{2}^{+}$ system.